I was curious also on this topic as I have a Samsung smartphone and a Galaxy Watch 3 as well as Buds Pro and read that the Samsung Wear App does not work with custom ROMs and checks if you have a Samung device - it works on non Samsung devices.
There is a solution using Magisk, however I don’t wanted to use this solution and try to edit build.prop using ADB instead.
Finally I was successful with this steps:
First you need to enable Developer Options and enable USB Debbuging as well as root access option using ADB in the Developer Options.
You also need to have ADB available on your OS (I used Mint Linux).
Then connect your smartphone with an USB Cable to you PC.
Check if your device is recognized: adb devices
Restart ADB as root: adb root
Download build.prop to your PC: adb pull /system/build.prop /home/YOURHOME
(adapt YOURHOME or use another directory to store the build.prop)
Now you can edit build.prop using your a text editor: change ro.product.brand“ and „ro.product.manufacturer“ from „samsung“ to e.g. „htc“
Upload build.prop to your device: adb push /home/YOURHOME/build.prop /system/build.prop
Fix permissions: adb shell chmod 644 /system/build.prop
Reboot your device: adb reboot
The Samsung Wear App should work now on your Samsung device
Regain your privacy! Adopt /e/ the unGoogled mobile OS and online services